The repair shop changed the parts ETA three times today. How can I talk to the customer without losing their trust?

Today, a small repair order got stuck because of parts. The supplier said they would arrive in the morning, then changed it to tomorrow in the afternoon, and the customer is already chasing us. Previously, just saying 'it hasn't arrived yet' made it seem like the shop wasn't following up. This time, I organized the supplier order number, the latest ETA, the risks of using substitute parts, and…